Conversion lenses and minimum focusing

The minimum focusing distance of a given lens (and it's focal length), is a constant regardless of sensor size.

So, as an example...I have a 14mm lens that focus down to 0.18m. If I add a .75 conversion lens on it...How close can I focus? And does one go about figuring it out? Can I still only focus down to 0.18m, even with the .75 lens attached? Maybe I could focus closer? If so, how do I calculate? Does the .75 converter lens has its own minimum focusing distance?

I think I misunderstood your question. I thought it was regarding using a lens on a smaller sensor. What's a conversion lens?

What's a conversion lens?

See here. Anyone?

My guess is #4 for an exact answer.

With a rear mounted TC it's easy. The minimum focus distance of the lens doesn't change at all.

Since most front conversion lenses are either (low quality) or (b) low power I suspect that there isn't a huge change in focus distance. However I know from experience that adding a 1.5x front conversion lens to a lens on one camera I own increases the minimum focus distance by about 50%.

The only thing you can say for sure about most front conversion lenses is that they don't work very well as far as image quality goes. There are a few pretty expensive ones custom designed to work with a particular lens that may not be too bad, but in general (especially with the wide angle ones), the image quality significantly degrades as you move away from the center of the image. The mild telephoto ones (say 1.5x) usually work better than the wideangle ones.

The results I have found with front attached conversion lenses have been at best poor with reduced resolution especially at the corners. To be fair, these lenses were generic and not specifically formulated for any particular lens. Some manufactures lenses that are computed to work with one lens could be better although of course more expensive. As to minimum focus I am not sure but I think it varies with the lens. I don't know of a formula but if you could try the lens, then with through the lens viewing it would be easy to quickly determine minimum focus and field size. With the auxiliary lenses I have tried focus was changed from the scale on the lens both for wide angle and telephoto conversion types. Personally, from my admittedly limited experience I would not consider any of these lenses for serious work.

I'm not sure where you are coming from but I suggest if you want tight framing then you add a close-up lens to a longer focal length lens to overcome the problem that they have limited extension to focus close .. else if you can you would provide extra extension in the rig.
To add a wide-angle adaptor and then want to come close with it is a bit nonsensical to me. Unless you are after the perspective that approach would achieve.
To add a telephoto adaptor makes some sense. But adding both an adaptor and a close-up lens is not likely to achieve that great IQ, though the reverse of statements above is that opten the central portion of a photo taken with an adaptor is quite reasonable. If you are after tight framing and have the resolution to spare the adaptor coupled with cropping is a reasonable way to go.
Your approach is detirmined probably as to if you have an interchangeable lens camera or a fixed lens camera and the answer varies accordingly.
I appreciate I probably have completely misunderstood your question :-)

You might have better luck asking on a video-dedicated forum, as conversion lenses seem to be much more popular on camcorders, compared to still cameras.
Off the top of my head, I'd hazard a guess that there is a formula, but you'd need experience to figure it out...

It is complex, especially with zoom lenses. Also, we are often lack of information about our lenses (even prime lenses). For a start, say we can look at
http://en.wikipedia.org/wiki/Lens_(optics)#Compound_lenses
we need formulas for compound lenses and all our lenses now are compound. We need to know the BFL (back focal length) of our lens (which is changing in zoom lenses) to calculate the new focal length and BFL of the combination of our lens with the converter.
Bottom line is when we attach the converter, focal length and bfl change. That makes the closest distance changes (the farthest, infinity focus may be lost too)